Why do you multiply by the reciprocal when dividing fractions

Asked by admin @ 26/11/2021 in Mathematics viewed by 268 People

Complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions. Find 1/4 ÷ 3/8. ....................................................................................................................................................

Step 1:rewrite it as 1/4/3/8. ....................................................................................................................................................Step 2:multiply the numerator and the denominator by the reciprocal of blank /blank. 1/4/3/8=1/4/3/8×blank/blank/ blank /blank. ....................................................................................................................................................Step 3:simplify the denominator 1/4×8/3/blank .................................................................................................................................................Step 4:simplify the fraction blank/blank ×blank/blank.

Answered by admin @ 26/11/2021

To complete
the steps to demonstrate why you multiply by the reciprocal when
dividing fractions.

To find
$\frac{1}{4}\div\frac{3}8}$

Step 1:
Rewrite it as
$\frac{\frac{1}{4}}{\frac{3}{8}}$ .

Step
2:
Multiply the numerator and the denominator by the reciprocal of
$\frac{3}{8}$ .

$\frac{\frac{1}{4}}{\frac{3}{8}}=\frac{\frac{1}{4}}{\frac{3}{8}}\times\frac{\frac{8}{3}}{\frac{8}{3}}$

Step
3:
Simplify the denominator
$\frac{\frac{1}{4}\times\frac{8}{3}}{1}$

Step
4:
Simplify the fraction
$\frac{1}{4}\times\frac{8}{3}$ .

We complete the solution as follows:
$\frac{1}{4}\times\frac{8}{3}=\frac{1\times8}{4\times3}\\ \\=\frac{8}{12}=\frac{4\times2}{4\times3}=\frac{2}{3}$

Why do you multiply by the reciprocal when dividing fractions

Similar Questions

How to multiply and divide by 10 100 and 1000

Lesson 3 10 practice b dividing fractions and mixed numbers

How to multiply and divide decimals by powers of 10

How do you divide a whole number by a fraction

How to solve a whole number divided by a fraction

How to divide fractions with square roots in the numerator

How do i divide a whole number by a fraction

How to multiply fractions with different denominators step by step

Multiply 6 13 by the reciprocal of by 16

Multiply 6 13 by the reciprocal of 7 16

What is the reciprocal of 2 9 in a fraction

What is the reciprocal of 6 7 in fraction form

What is the reciprocal of 5 6 in fraction form

What is the reciprocal of 8 9 as a fraction

What is the reciprocal of 5 8 in fraction form

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220