Subtracting Fractions with Different Denominators
Students will be able to subtract fractions with unlike denominators.
- Write ⅘ − ⅕ on the board and ask students to solve for the problem on their whiteboards using whatever method they choose.
- Have students share their answers with their elbow partner. Gather their background knowledge by asking them questions about the numerator, denominator, and how they got their answer.
- Ask for a volunteer to come to the board and solve the problem using a number line, area model, or simply subtracting one-fifth from four-fifths.
- Tell students that today they'll build on their understanding of subtracting fractions with like denominators to subtract fractions with unlike denominators.
Explicit Instruction/Teacher modeling(8 minutes)
- Remind students that the denominator is the bottom number of a fraction and represents the total number of pieces of the whole, while the numerator is the top number and represents some of the parts of the whole (e.g., ⅖ represents 2 pieces of the total 5 pieces).
- Write ⅘ − ⅒ on the board. Explain that the denominator is different so they cannot subtract the number 1 from the number 4. Tip: draw bar models of ⅘ and ⅒ to show that the total parts, or whole, (i.e., denominator) is different, so if they subtracted the number 1 from ⅘ it would subtract too much.
- Think aloud finding multiples for the denominators 5 (e.g., 5, 10, 15, 20, 25, etc.) and 10 (e.g., 10, 20, 30, 40, etc.) and write them on the board. Explain to them that a multiple is the result of multiplying a number by an integer (e.g., 4 x 4 = 12, where 12 is the multiple).
- Consider the list of multiples and then circle the least common multiple, or the smallest multiple they have in common (i.e., 10). Then, think aloud how to change the 5 in the denominator to 10 (i.e., multiplying 5 by 2) and multiply by the number 2 on the top and bottom so that you get a new equation of 8⁄10 − ⅒.
- Subtract one-tenth from eight-tenths to get a total of seven-tenths remaining. Compare the final answer to what the answer would have been had you subtracted the equation using unlike denominators.
Guided Practice(15 minutes)
- Ask students to explain why it's important to change the denominators so that they are the same. Write some of their responses on the board.
- Write 5⁄8 − ¼ on the board and ask students to help you solve the problem. Call on students to tell you the next step and make some "mistakes" they have to correct along the way.
- Have a volunteer explain how to subtract fractions when they have different denominators. They should understand the following steps:
- Check to make sure the denominators are the same.
- If the denominators are not the same, find the least common multiple for the denominators.
- Multiply the denominator and numerator by the number that will make the denominator equal to the least common multiple.
- Subtract the fractions.
- Write the steps on the board for students to reference as they work with their partners to complete the first two problems from the Subtracting Fractions worksheet. Ask students to use their whiteboards to complete the problems.
Independent working time(12 minutes)
- Distribute the first page of the Subtracting Fractions worksheet and ask students to complete the problem on their own. Remind them to use the steps written on the board if they get stuck and do not know what to do next.
- Have them share their answers with mixed ability groups and adjust them as necessary. If partners had to adjust their answers often, provide further explanation to the group and ask the students to restate your explanation.
- Allow one student to share a problem and ask the other students to critique the process the presenter used to subtract the problem.
- Have students multiply the denominators by each other and then do the same to the numerators instead of finding the least common multiple. See the Fraction Word Problems: Subtracting with Unlike Denominators worksheet for an example.
- Allow them to work in a small, teacher-led group with manipulatives as they create their common multiples and subtract the fractions.
- Provide sentence frames and a key words list for the student explanations throughout the lesson.
- Have students use the Subtraction Challenge page from the Subtracting Fractions worksheet to create their own subtraction problems. Challenge them to subtract the smaller fraction by the larger fraction and to show their work using bar models and by finding the least common multiple. Increase the challenge further by using more dice to find the denominator.
- Pair them with struggling learners and ask them to explain their process to the students.
- Distribute a lined sheet of paper and write 11⁄12 − ¾ on the board. Ask students to solve the problem and write down their process.
- Allow students to share their answer to the subtraction problem and their written explanation aloud to their partners. Give them the opportunity to make any adjustments as necessary.
Review and closing(5 minutes)
- Ask students to explain why it's important to only subtract fractions that have the same denominators.
- Explain that understanding how to subtract simple fractions correctly will help them when they have to subtract mixed numbers.