Understanding fractions as parts of a whole
A fraction represents part of a whole thing or a whole group. The denominator (bottom number) shows the total number of equal parts the whole is divided into. The numerator (top number) shows how many of those parts you have.
- "Liam and his mom baked a blueberry pie. They cut the pie into 6 equal slices for dessert. What fraction of the whole pie is one slice?"
- Whole: The pie.
- Equal Parts: 6 slices (this is the denominator).
- Part We Have: 1 slice (this is the numerator).
- The fraction is 16.
First, ask: "What is the whole?" Then, find out how many equal parts it's split into. This is the most important step in solving any fraction word problem.
Finding a fraction of a group
Sometimes the "whole" isn't one object, like a pie, but a group of things, like crayons or students. You find the fraction by comparing the number of items in the part you want to the total number of items in the group.
- "A box of crayons has 4 red crayons, 3 blue crayons, and 1 green crayon. What fraction of the crayons in the box are blue?"
- Step 1 (The Whole): Find the total crayons. 4 + 3 + 1 = 8 crayons (denominator).
- Step 2 (The Part): Identify the specific part. There are 3 blue crayons (numerator).
- Step 3 (The Fraction): Blue crayons are 38 of the box.
When the problem describes a group with different types, always start by adding to find the total. That total is your denominator.
Finding the fraction that is left
A common type of problem gives you a total, tells you how much was used or taken away, and asks what fraction is remaining.
- "Ms. Gomez graded 5 tests on Monday and 2 tests on Tuesday. She had a total of 10 tests to grade. What fraction of her total tests does she still need to grade?"
- Step 1 (The Whole): Total tests = 10 (denominator).
- Step 2 (The Part We Want): First, find how many are left. Tests graded: 5 + 2 = 7. Tests left: 10 - 7 = 3 (numerator).
- Step 3 (The Fraction): The fraction of tests left is 310.
The fraction is always based on the original total (10 tests), not the amount that is gone. You must calculate the "leftover" amount to be the numerator.
Simplifying fractions to their easiest form
A fraction is in simplest form when the numerator and denominator have no common factors other than 1. We simplify to make fractions easier to understand and compare.
- "A baker made a tray of 12 cookies. She put chocolate chips in 4 of the cookies and walnuts in the rest. What fraction of the cookies have walnuts?"
- Step 1: Find the part. Walnut cookies: 12 - 4 = 8.
- Step 2: Write the fraction: 812.
- Step 3 (Simplify): Find the largest number that divides evenly into both 8 and 12. That number is 4.
- Divide the numerator and denominator by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
- The simplified fraction is 23.
Look for a number you can divide into both the top and bottom. Keep dividing until the only common factor is 1. In the practice, you'll simplify fractions like 1848 to 38 and 1560 to 14.
Solving problems with larger numbers
You can solve fraction problems with any size numbers using the same steps. The challenge is often the simplification step at the end.
- "A bus has 48 seats. At the first stop, 18 passengers get on and fill some seats. What fraction of the total seats are now filled?"
- Step 1 (Whole): 48 seats (denominator).
- Step 2 (Part): 18 filled seats (numerator). Fraction = 1848.
- Step 3 (Simplify): What is the largest number that divides into both 18 and 48? 6 works (18 ÷ 6 = 3, 48 ÷ 6 = 8).
- The simplest answer is 38 of the seats are filled.
For "Advanced" problems, remember: 1) Find the total (whole). 2) Find the specific part. 3) Write the fraction. 4) Always simplify your answer! The practice will help you master these steps.