Add, take away, multiply and divide fractions with bars and pictures. Solve missions, crack puzzles and beat the clock.
Start here. A fraction is a number of equal pieces out of a whole. In 3/8 the bottom (denominator) says the whole is cut into 8 equal pieces and the top (numerator) says we have 3 of them.
Same-size pieces. If the pieces are the same size you can just count them. 3/8 + 2/8 is 3 pieces and 2 pieces, which is 5 pieces of size 1/8. So the answer is 5/8. Add or take away the tops. The bottom stays the same.
Improper fractions and mixed numbers. When the top is bigger than the bottom, you have more than one whole. 7/4 is 7 quarter-pieces. Four of them fill one whole bar, and 3 are left over, so 7/4 = 1 3/4. To go back, multiply the whole by the bottom and add the top: 1 × 4 + 3 = 7 pieces.
Different-size pieces. To add 1/2 + 1/3 the pieces are different sizes. Cut both bars into 6 equal pieces: 1/2 = 3/6 and 1/3 = 2/6. Now add: 3/6 + 2/6 = 5/6. The new bottom, 6, is the common denominator. The smallest one is the smallest number that both bottoms divide into.
Lowest terms. 4/8 and 1/2 are the same amount. A fraction is in lowest terms when the top and the bottom cannot be divided by the same number any more. Divide both by the biggest number that fits into both.
Multiplying. A fraction times a whole number means groups: 3 × 2/5 is three groups of 2/5, which is 6/5. A fraction times a fraction means "of": 1/2 of 3/4. Cut a square into columns and rows and look at the overlap: multiply the tops and multiply the bottoms.
Dividing. Dividing asks "how many fit?". How many 1/4s fit into 3? Each whole bar has 4 quarters, so 3 bars have 12 quarters. In short, to divide by a fraction you flip it and multiply: 3 ÷ 1/4 = 3 × 4 = 12.
First cut both bars into equal pieces of the same size, which means finding a common denominator. For 1/4 + 1/6 use twelfths: 3/12 + 2/12 = 5/12. Then add the tops and simplify if you can.
It is a number that both bottom numbers divide into. The smallest one makes the numbers easiest to work with. For 1/4 and 1/6 the smallest common denominator is 12.
They show the same amount in two ways. An improper fraction like 9/4 has a top bigger than its bottom. A mixed number like 2 1/4 shows the whole bars and the leftover pieces.
Dividing by 1/4 asks how many quarters fit in a bar, and the answer is 4 per bar. That is the same as multiplying by 4, the flipped fraction 4/1. Dividing by a fraction and multiplying by its flip give the same answer.
Just starting: same-size pieces, improper fractions and mixed numbers. I know the basics: different bottoms and common denominators. Challenge me: multiplying, dividing and recipe problems.
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