Fractions and Equivalent Fractions

A fraction names a part of a whole or a part of a group. The bottom number (the denominator) tells you how many equal parts the whole is split into. The top number (the numerator) tells you how many of those parts you are talking about. Two fractions can look different yet stand for exactly the same amount — those are called equivalent fractions.

Reading a Fraction

• The denominator is on the bottom — it counts the equal pieces in one whole.
• The numerator is on the top — it counts the pieces being shaded or used.
• Read 3/4 as "three-fourths" — three out of four equal parts.
• A fraction bar between the numerator and denominator means division: 3/4 means 3 divided by 4.

Building Equivalent Fractions (Multiplying)

• Multiply the numerator AND the denominator by the same non-zero number.
• 1/2 multiplied by 2/2 gives 2/4 — the value is the same because 2/2 equals 1.
• 1/2 multiplied by 4/4 gives 4/8 — still the same amount, just cut into more pieces.
• If you only multiply one of them, the value of the fraction changes.

Simplifying a Fraction (Dividing)

• Divide the numerator AND the denominator by their greatest common factor (GCF).
• For 6/8 the GCF of 6 and 8 is 2: 6 divided by 2 is 3, 8 divided by 2 is 4, so 6/8 equals 3/4.
• A fraction is in simplest form when the GCF of its numerator and denominator is 1.
• Never add or subtract from the top and bottom — only multiply or divide by the same number.

Checking if Two Fractions Are Equivalent

• Cross-multiply: a/b equals c/d if a times d equals b times c.
• Is 3/4 the same as 9/12? Check: 3 times 12 is 36, and 4 times 9 is 36 — yes, equivalent.
• You can also simplify both fractions; if they reduce to the same lowest-terms fraction, they are equivalent.
• Drawing two bars or circles with the same shaded area is another way to prove it.