Question

u5, l10: dividing decimals by decimals: algorithm
homework

1. here is how han found 31.59 ÷ 13:

a. explain how han solved.

b. check that han’s answer is correct by calculating the product of 2.43 and 13.

1. divide: 3.85 ÷ 1.4

Explanation:

1a. Brief Explanations:

Han used long division:

1. Divided 31 by 13, got 2, multiplied 13×2=26, subtracted from 31 to get 5.
2. Brought down the 5 (tenths place) to make 5.5. Divided 5.5 by 13 to get 0.4, multiplied 13×0.4=5.2, subtracted to get 0.3.
3. Brought down the 9 (hundredths place) to make 0.39. Divided 0.39 by 13 to get 0.03, multiplied 13×0.03=0.39, subtracted to get 0.
4. Combined the quotient parts: 2 + 0.4 + 0.03 = 2.43.

1b. Step-by-Step Format:

Step1: Split 2.43 into parts

$2.43 = 2 + 0.4 + 0.03$

Step2: Multiply each part by 13

$2×13=26$, $0.4×13=5.2$, $0.03×13=0.39$

Step3: Sum the products

$26 + 5.2 + 0.39 = 31.59$

Answer:

The product equals 31.59, so Han's answer is correct.

2. Step-by-Step Format:

Step1: Rewrite division to eliminate decimals

Multiply numerator and denominator by 10: $\frac{3.85×10}{1.4×10} = \frac{38.5}{14}$

Step2: Perform long division

14 goes into 38 twice ($14×2=28$), subtract: $38-28=10$. Bring down 5 to get 105.
14 goes into 105 7.5 times ($14×7=98$, $14×0.5=7$; $98+7=105$)

Step3: Combine quotient parts

$2 + 0.75 = 2.75$