Adding and subtracting fractions with the same bottom number within one whole
Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
What a learner can do afterwards
- Calculate 2/5 + 2/5 = 4/5
- Calculate 6/8 − 3/8 = 3/8
- Explain that when denominators are the same, you add/subtract the numerators
1 · Read
The bottom number, or denominator, counts equal parts in one whole. The top number, or numerator, counts the parts you have. Use the same whole or unit when joining amounts. With matching bottom numbers, add the tops and keep the bottom. To find a missing added part, subtract the known part from the total.
To subtract matching fractions, take away the top numbers and keep the bottom. For 7/9 - 2/9, count seven ninths and remove two. Five ninths remain: 7/9 - 2/9 = 5/9.
A ribbon measures 5/7 meter. Ravi cuts off 1/7 meter. The pieces are sevenths of a meter, so 5 - 1 leaves four of them: 4/7 meter. For two cuts, subtract each cut in turn from the amount left.
Check the bottom numbers before counting pieces together. Fifths join directly with fifths. Fifths and fourths are different-size parts of the same whole. Those parts need a new matching name before you can add their top numbers.
Adding matching fractions does not recut the whole. For 1/6 + 2/6, the three pieces are still sixths: 3/6. Adding the bottoms would name twelfths instead, which are smaller pieces. Keep the original piece size by keeping the bottom number.
In a measuring story, name the whole you are using. If a jug holds seven cups, each cup is 1/7 of its capacity. Four cups of juice are 4/7 of that capacity. Pouring out one cup leaves three cups, or 3/7 of the jug's capacity.
Taking away all of an amount leaves zero. Subtract matching top numbers to get 0, and keep the bottom number. To write a joining story as an equation, put each amount beside a plus sign, then write the total after the equals sign.
Same bottom number? Just add or subtract the top numbers, and keep the bottom number the same.
Lesson, questions and flashcards written for this learning dataset.
Practice questions and readings written for this learning dataset. Includes fraction flashcards retained from the existing collection.
2 · Watch
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