Question

Find the quotients
a) 0.765 / 1.5
b) 0.666 / 1.11
c) 1.875 / 2.5
d) 3.024 / 0.36
e) 3.192 / 0.2

Answer 1

Answer:

a) 0.765 / 1.5 = 51/ 100

= 0.51

b) 0.666 / 1.11 = 3/ 5

= 0.6

c) 1.875 / 2.5 = 3/ 4

= 0.75

d) 3.024 / 0.36 = 42/ 5

= 8 2/ 5

= 8.4

e) 3.192 / 0.2 = 399/ 25

= 15 24/ 25

= 15.96

Step by step:

How do you solve decimals step by step?

Conversion a decimal number to a fraction: 0.765 = 765/ 1000

= 153/ 200

a) Write down the decimal 0.765 divided by 1: 0.765 = 0.765/ 1

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

0.765/ 1

= 7.65/ 10

= 76.5/ 100

= 765/ 1000

Note: 765/ 1000  is called a decimal fraction.

c) Simplify and reduce the fraction

765/ 1000

= 153 * 5/

200 * 5

= 153 * 5/ 200 * 5

= 153/ 200

Conversion a decimal number to a fraction: 1.5 = 15/ 10

= 3/ 2

a) Write down the decimal 1.5 divided by 1: 1.5 = 1.5/ 1

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

1.5/ 1

= 15/ 10

Note: 15/ 10  is called a decimal fraction.

c) Simplify and reduce the fraction

15/ 10

= 3 * 5/ 2 * 5

= 3 * 5/ 2 * 5

= 3/ 2

Divide: 0.765 / 1.5 = 153/ 200  · 2/ 3

= 153 · 2/ 200 · 3

= 306/ 600

= 6 · 51/ 6 · 100

= 51/ 100

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/

2  is 2/ 3 ) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 6 gives 51/ 100 .

In words - one hundred fifty-three two-hundredths divided by three halfs = fifty-one one-hundredths.