Divide a decimal by a decimal

### 1.1. Knowledge to remember

**a)** __Example 1__: An iron bar is 6.2 dm long and weighs 23.56 kg. How many kilograms does 1dm of that iron rod weigh?

We have to do the division: 23.56 : 62 = ?

We have: 23.56 : 6.2 = (23.56 x 10) : (6.2 x 10)

23.56 : 6.2 = 235.6 : 62

Usually we set the calculation and then do the following:

- The decimal part of the number 6.2 has one digit.
- Move the comma of the number 23.56 to the right by one digit to get 235.6; Remove the comma at 6.2 to get 62.
- Perform division 235.6 : 62

So 23.56 : 6.2 = 3.8 (kg)

**b)** __Example 2__: 82.55 : 1.27 = ?

We calculate and then do the following:

- The decimal part of two numbers 82.55 and 1.27 has two digits; remove the comma in those two numbers to get 8255 and 127
- Perform division 8255 : 127

*** To divide a decimal by a decimal, do the following:

- Count how many digits are in the decimal part of the divisor, then move the decimal point of the divisor to the right by as many digits.
- Remove the comma from the divisor and then perform the division as if it were a natural number.

### 1.2. Solve textbook exercises on page 71

**Lesson 1 **

Calculate then calculate:

a) 19.72:5.8 b) 8.216:5,2

c) 12.88:0.25 d) 17.4:1.45

__Solution guide:__

Lesson 2

Knowing 4.5l of oil weighs 3.42kg. How many kilograms does 8 liters of oil weigh?

__Solution guide:__

1 liter of kerosene weighs kilograms:

3.42 : 4.5 = 0.76(kg)

8l

$8l$kerosene weighing kilograms is:

0.76 × 8 = 6.08(kg)

Answer: 6.08kg.

lesson 3

Sew a set of clothes with 2.8m of fabric. Ask 429.5m of fabric, how many such clothes can be sewn at most and how many meters of fabric are left?

__Solution guide:__

We have:

429.5 : 2.8 = 153 (remainder 1.1)

So if there is 429.5m of fabric, the shop can sew 153 sets of clothes and has 1.1m of fabric left over.

Answer: 153 suits; 1.1m of fabric left over.

### 1.3. Solve the exercises in the textbook Practice page 72

Lesson 1

Calculate then calculate:

a)17.55:3.9 b)0.603:0.09

c)0,3068:0.26 d)98,156:4.63.

__Solution guide:__

Lesson 2

Find x:

a) x × 1.8 = 72

b) x × 0.34 = 1.19 × 1.02

c) x × 1.36 = 4.76 × 4.08.

__Solution guide:__

\(\begin{array}{l}

a)x \times 1.8 = 72\\

x = 72:1.8\\

x = 40\\

b)x \times 0.34 = 1.19 \times 1.02\\

x \times 0.34 = 1.2138\\

x = 1.2138:0.34\\

x = 3.57\\

c)x \times 1.36 = 4.76 \times 4.08\\

x \times 1.36 = 19.4208\\

x = 19.4208:1.36\\

x = 14.28

\end{array}\)

lesson 3

Knowing 5.2l of oil weighs 3,952. How many liters of oil are there if they weigh 5.32kg?

__Solution guide:__

$\mathrm{first}l$

kerosene weighing kilograms is:

3.952 : 5.2 = 0.76(kg)

The number of liters of oil is:

5.32 : 0.76 = 7(l)

Answer: 7 liters of kerosene.

**Lesson 4**

Find the remainder of the division 218 : 3.7 if only two digits are taken in the decimal part of the quotient.

__Solution guide:__

Draw a line from the digit 8

$8$in the units row of the number being divided (as shown in the figure above) we see the remainder is 0.033

Retry: 58.91 × 3.7 + 0.033 = 217,967 + 0.033 = 218

So the remainder of the division of 218 : 3.7 if only two digits are taken in the decimal part of the quotient is 0.033.

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