Fractions are the part of mathematics that helps us to determine the part of a whole or equal parts. It contains the upper part known as the numerator and the lower part known as the denominator.
In this article, we will be going to learn how to solve comparing fractions.
What are comparing fractions?
Comparing Fractions: To compare fractions, either convert them to like fractions (fractions with the same denominator) or convert them to decimals and compare the decimal values.
Comparing Fraction important concept
Cross Multiplication: Multiply the numerator of each fraction by the denominator of the other fraction. Compare the products.
Example: Compare 7/4 and 9/5.
Solution:
Cross Multiply: Multiply the numerator of each fraction by the denominator of the other fraction:
7×5=35
4×9=36
Compare the Products:
Since 35<36, we conclude that 7/4<9/5.
Thus, 7/4<9/5.
Finding Common Denominators: Convert the fractions to equivalent fractions with the same denominator and then compare the numerators.
Example: Compare 3/4 and 5/6.
Solution:
Find the Least Common Denominator (LCD):
The denominators are 4 and 6.
The least common denominator is the least common multiple (LCM) of 4 and 6.
The LCM of 4 and 6 is 12.
Convert the Fractions to Have the Same Denominator:
For 3/4, multiply both the numerator and the denominator by 3 to get: 3/4=9/12
For 5/6, multiply both the numerator and the denominator by 2 to get: 5/6=10/12
Compare the Numerators:
Now, compare 9/12 and 10/12.
Since 9<10, we conclude that 3/4<5/6.
Thus, 3/4<5/6.
Comparing Fractions: Solved problems
Problem 1: Compare 3/ and 2/3.
Solution:
Cross multiply: 3×3=9and5×2=10
Since 9<10, 3/5<2/3.
Problem 2: Compare 4/7 and 4/9.
Solution:
Fractions with the same numerator can be compared by looking at their denominators. The fraction with the smaller denominator is larger.
Since 7<9, 4/7>4/9.
Problem 3: Compare 1/8 and 1/6.
Solution:
Unit fractions are fractions with a numerator of 1. The larger the denominator, the smaller the fraction.
Since 8>6, 1/8<1/6.
Problem 4: Compare
Solution:
Both have the same whole number part (2), so compare the fractional parts 1/3 and 1/4.
Since 1/3>1/4,
2 \frac{1}{3} > 2 \frac{1}{4} .
Problem 5: Compare 7/4 and 9/5.
Solution:
Cross multiply: 7×5=35and4×9=36
Since 35<36, 7/4<9/5.
Problem 6: Compare 5/8 and 3/5 by converting to decimals.
Solution:
Convert both fractions to decimals: 5/8=0.625and3/5=0.6
Since 0.625>0.6, 5/8>3/5.
Problem 7: Compare 13/20 and 17/25.
Solution:
Cross multiply: 13×25=325and20×17=340
Since 325<340, 13/20<17/25
Problem 8: Compare 5/6 and 7/8.
Solution:
Find the least common denominator (LCD), which is 24.
Convert both fractions: 5/6=20/24and7/8=21/24
Since 20<21, 5/6<7/8.
Problem 9: Compare −3/4 and 1/2.
Solution:
Any positive fraction is greater than a negative fraction.
Therefore, 1/2>−3/4.
Problem 10: Compare 2/4 and 1/2.
Solution:
Simplify 2/4 to 1/2.
Since both fractions are equal, 2/4=1/2.
Worksheet: Fractions
Problem 1: Compare which one is greater fraction:
Problem 2: Compare which one is smaller fraction
Problem 3: Compare which one is greater,=,less fraction
Problem 4: Compare which one is smaller fraction
Problem 5: Compare which one is greater,=,less fraction
Problem 6: Compare which one is smaller fraction
Problem 7: Compare the fraction
Problem 8: Compare which one is smaller fraction
Problem 9: Compare which one is greater fraction
Problem 10: Compare which one is smaller fraction
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