🔢 Equivalent Fractions

What is a Fraction?
A fraction names a part of a whole. It is written as numeratordenominator. The denominator (bottom number) tells how many equal parts the whole is divided into; the numerator (top number) tells how many of those parts we take. So 34 means 3 out of 4 equal parts.
What are Equivalent Fractions?
Equivalent fractions are fractions that look different but name the same amount. For example 12, 24 and 48 all cover exactly half of a bar they are equivalent.
How to Make an Equivalent Fraction
Multiply or divide the numerator and the denominator by the same non-zero number. Whatever you do to the top, you must do to the bottom:
12=1×2/2×2=24=1×3/2×3=36
Simplest Form
A fraction is in simplest form when the top and bottom share no common factor except 1. To simplify, divide both by their highest common factor. For example 68=6÷28÷2=34.
Fraction×…

Comparing fractions means deciding which one is larger (or whether they are equal). There are three simple cases.
Case 1 Same denominator. If the bottoms are equal, the fraction with the bigger numerator is bigger: 35>25.
Case 2 Same numerator. If the tops are equal, the fraction with the smaller denominator is bigger fewer pieces means each piece is larger: 14>18.
Case 3 Unlike denominators. Make the denominators the same first, then compare the tops:
• Find a common denominator (usually the LCM of the two denominators).
• Rewrite each fraction as an equivalent fraction with that denominator.
• Compare the numerators.

Example: compare 23 and 34. The LCM of 3 and 4 is 12:
23=8/12 34=9/12⇒ 34>23
Benchmark trick. Compare each fraction to 12. Since 38 is less than 12 and 58 is more than 12, we know 58>38 without any calculation.
Symbols: > means greater than, Common…

When two fractions have the same denominator, adding or subtracting them is easy: keep the denominator and just add (or subtract) the numerators.
a/d+b/d=a+b/d a/d-b/d=a-b/d
Why the bottom stays the same: the denominator tells the size of each piece. When we put pieces together or take some away, the size of a piece does not change only how many we have changes. So only the numerators are added or subtracted.
Examples: 15+25=35 and 45-15=35.
Always simplify the answer when you can:
26=2÷2/6÷2=13
Improper fractions. If the top becomes bigger than the bottom, the answer is more than one whole. For example 35+45=75, which is the same as 125.
Common mistake to avoid: do not add the denominators. 15+25 is 35, never 310.