Lý thuyết Hai bài toán về phân số (Cánh diều 2024) Toán 6

Lý thuyết Toán lớp 6 Bài 10: Hai bài toán về phân số

A. Lý thuyết Hai bài toán về phân số

1. Tìm giá trị phân số của một số cho trước

- Muốn tìm giá trị $\frac{m}{n}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}$ của số a cho trước, ta tính $a.\frac{m}{n}$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">.</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}$$\left(m\in N,n\in N*\right)$$\left(\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\in </span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\mathbb{N}</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\in </span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\mathbb{N}</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">*</span></span></span>\right)$  .

Giá trị của m% của số a là giá trị phân số $\frac{m}{100}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}$ của số a.

- Muốn tìm giá trị m% của số a cho trước, ta tính $a.\frac{m}{100}\left(m\in N*\right)$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">.</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}\left(\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\in </span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\mathbb{N}</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">*</span></span></span>\right)$.

Ví dụ 1.  Tính:

a) $\frac{2}{3}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">2</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}$ của 8,7;

b) 25% của 328 mét.

Hướng dẫn giải

a) $\frac{2}{3}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">2</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}$ của 8,7 là: $8,7.\frac{2}{3}=\frac{8,7.2}{3}=5,8$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">8</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">7.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">2</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">8</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">7.2</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">8</span></span></span>}$;

b) 25% của 328 mét là: $328.\frac{25}{100}=328.\frac{1}{4}=82$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">328.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">25</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">328.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">4</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">82</span></span></span>}$ (m).

2. Tìm một số biết giá trị phân số của số đó

- Muốn tìm một số biết $\frac{m}{n}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}$ của nó bằng a, ta tính $a:\frac{m}{n}\left(m,n\in N*\right)$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">:</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}\left(\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\in </span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\mathbb{N}</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">*</span></span></span>\right)$.

- Muốn tìm một số biết m% của nó bằng a, ta tính $a:\frac{m}{100}\left(m\in N*\right)$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">:</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}\left(\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">�</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\in </span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\mathbb{N}</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">*</span></span></span>\right)$.

Ví dụ 2. Tìm một số, biết:

a) $\frac{5}{6}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}$ của nó bằng ‒80;

b) 47% của nó bằng $\frac{47}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ kg.

Hướng dẫn giải

a) $\frac{5}{6}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}$ của một số bằng ‒80 nên số đó là: $\left(-80\right):\frac{5}{6}=\left(-80\right).\frac{6}{5}=-96$$\left(<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">-</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">80</span></span></span>}\right)<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">:</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\left(<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">-</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">80</span></span></span>}\right)<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">.</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span><span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">-</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">96</span></span></span>}$  

b) 47% của một số bằng $\frac{47}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ kg nên số đó là: $\frac{47}{5}:\frac{47}{100}=\frac{47}{5}.\frac{100}{47}=20$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">:</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">.</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">47</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">20</span></span></span>}$ (kg).

B. Bài tập tự luyện

Bài 1. Một cửa hàng bán chiếc xe đạp với giá khuyến mãi giảm 15% so với giá niêm yết. Biết tin khuyến mãi nên mẹ đưa Bình ra cửa hàng mua cho chiếc xe đạp với giá 7 225 000 đồng. Hỏi chiếc xe đạp có giá niêm yết là bao nhiêu?

Hướng dẫn giải

Vì chiếc xe đạp được giảm 15% so với giá niêm yết nên mẹ Bình đã mua chiếc xe đó bằng 85% giá niêm yết.

Giá niêm yết của chiếc xe là:

7 225 000 : 85% =  $\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">7225000</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">:</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">85</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">7225000.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">85</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">8500000</span></span></span>}$(đồng)

Bài 2. Tính:

a) $\frac{4}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">4</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ của ‒60;

b) 75% của 16;

c) $\frac{1}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ của 225 000 đồng;

d) Có bao nhiêu phút trong $\frac{5}{12}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">12</span></span></span>}}$ giờ?

Hướng dẫn giải

a) $\frac{4}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">4</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ của ‒60 là: $\left(-60\right).\frac{4}{5}=-48$$\left(<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">-</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">60</span></span></span>}\right)<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">.</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">4</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span><span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">-</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">48</span></span></span>}$;

b) 75% của 16 là: $16.\frac{75}{100}=12$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">16.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">75</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">12</span></span></span>}$;

c) $\frac{1}{5}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}$ của 225 000 đồng là: 225 000 . $\frac{1}{5}=45000$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">45000</span></span></span>}$(đồng);

d) Ta có:  giờ = 60 phút

Số phút có trong  giờ là: 60. $\frac{5}{12}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">12</span></span></span>}}$ = 25 phút.

Bài 3. Tìm một số, biết:

a) $\frac{3}{25}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">25</span></span></span>}}$ của nó bằng 120;

b) 0,015 của nó bằng ‒30;

c) 120% của nó bằng 9 lít;

d) 6% của nó bằng 102 cây.

Hướng dẫn giải

a) $\frac{3}{25}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">25</span></span></span>}}$ của một số bằng 120 nên số đó là: 120 : $\frac{3}{25}=120.\frac{25}{3}=1000$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">25</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">120.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">25</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1000</span></span></span>}$;

b) 0,015 của nó bằng ‒30 nên số đó là: (‒30) : 0,015 = ‒2 000;

c) 120% của nó bằng 9 lít nên số đó là: 8 : $\frac{120}{100}=9.\frac{100}{120}=7,5$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">120</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">9.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">120</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">7</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}$(lít)

d) 6% của nó bằng 102 cây nên số đó là: 102 : $\frac{6}{100}=102.\frac{100}{6}=1700$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">102.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">6</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1700</span></span></span>}$ (cây)

Bài 4. Nguyên liệu để muối dưa cải gồm rau cải, hành tươi, đường và muối. Khối lượng hành, đường và muối theo thứ tự bằng 5%, $\frac{1}{1000}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1000</span></span></span>}}$ và $\frac{3}{40}$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">40</span></span></span>}}$ khối lượng của rau cải. Vậy nếu muối 3 kg rau cải cần bao nhiêu ki – lô – gam hành, đường và muối?

Hướng dẫn giải

Số ki – lô – gam hành cần là: 3.5% = $3.\frac{5}{100}=0,15$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">5</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">0</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">15</span></span></span>}$ (kg)

Số ki – lô – gam đường cần là: $3.\frac{1}{1000}=0,003$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">1000</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">0</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">003</span></span></span>}$ (kg)

Số ki – lô – gam muối cần là: $3.\frac{3}{40}=0,225$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">3</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">40</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">0</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">225</span></span></span>}$ (kg)

Vậy để muối 3 kg rau cải cần 0,15 kg hành; 0,003 kg đường và 0,225 kg muối.

Bài 5. Bố Lan gửi tiết kiệm 100 triệu đồng tại một ngân hàng theo kì hạn 12 tháng với lãi suất là 0,51% một tháng (tiền lãi mỗi tháng bằng 0,51% số tiền gửi ban đầu và sau 12 tháng mới được lấy lãi).

a) Hỏi hết thời hạn 12 tháng, bố Lan lấy cả gốc lẫn lãi được bao nhiêu?

b) Giả sử hết kì hạn 12 tháng, bố Lan không rút gốc và lãi thì sau 1 năm nữa, bố Lan rút cả gốc lẫn lãi là bao nhiêu? Biết rằng lãi suất không thay đổi.

Hướng dẫn giải

Ta có $0,51\%=\frac{0,51}{100}=\frac{51}{10000}$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">0</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">51</span></span></span>}\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">\%</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">0</span></span></span>}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">,</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">51</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">51</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">10000</span></span></span>}}$ 

a) Số tiền lãi nhận được sau một tháng là:

$100000000.\frac{51}{10000}=510000$$\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">100000000.</span></span></span>}\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">51</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">10000</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">510000</span></span></span>}$ (đồng)

Số tiền lãi nhận được sau 12 tháng là: 510 000 . 12 = 6 120 000 (đồng)

Số tiền cả gốc lẫn lãi bố Lan lấy được sau 1 năm là:

100 000 000 + 6 120 000 = 106 120 000 (đồng)

b) Số tiền lãi nhận được sau một tháng (của năm thứ hai) là:

106 120 000 . $\frac{51}{10000}=541212$$\frac{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">51</span></span></span>}}{\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">10000</span></span></span>}}<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">=</span></span></span>\mathrm{<span\; style="font-size:18px;"><span\; style="font-size:11px;"><span\; style="line-height:2;">541212</span></span></span>}$ (đồng)

Số tiền lãi nhận được sau 12 tháng là: 541 212 . 12 = 6 494 544 (đồng)

Số tiền cả gốc lẫn lãi bố Lan lấy được sau 2 năm là:

106 120 000 + 6 494 544 = 112 614 544 (đồng)

Vậy số tiền bố Lan nhận được khi lấy cả gốc lẫn lãi sau 2 năm là 112 614 544 đồng.