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Mastering Subtraction of Mixed Numbers with Renaming Techniques

In this lesson, students will learn how to accurately subtract mixed numbers that involve renaming. The process includes understanding the least common denominator (LCD), renaming fractions when necessary, and performing the subtraction step-by-step. Students will follow clear directions to write, rename, and simplify their problems. They will practice with examples, including how to borrow from whole numbers when the top fraction exceeds the bottom. By the end of the lesson, students will confidently subtract mixed numbers, ensuring that their answers are in the simplest form.

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Mastering Subtraction of Mixed Numbers with Renaming Techniques

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  1. Objective: Students will be able to subtract mixed numbers involving renaming (6-6).

  2. Vocabulary: • None

  3. Steps: • Read all directions!!!!!!!! • Write the problem. • Find the LCD (LCD=LCM). • Find new numerators. • Rename. • Subtract. • Simplify.

  4. Whole # and a fraction: • Rename by borrowing one from the whole #. • Add your numerator and denominator in top fraction only (this is your numerator). • Keep same denominator. • Subtract. • Simplify.

  5. Whole # only on top: • Rename by borrowing one from the whole number. • Next, look at the denominator in the bottom fraction. This becomes both your numerator and denominator. Second fraction stays the same. • Subtract. • Simplify.

  6. Examples Find 4 – 1 2/3 4 - 1 2/3

  7. Examples Find 4 – 1 2/3 4 3 3/3Rename 4 as 3 3/3. - 1 2/3- 1 2/3

  8. Examples Find 4 – 1 2/3 4 3 3/3 Rename 4 as 3 3/3. - 1 2/3- 1 2/3 1/3Subtract the fractions

  9. Examples Find 4 – 1 2/3 4 3 3/3 Rename 4 as 3 3/3. - 1 2/3- 1 2/3 2 1/3 Subtract the fractions Then subtract the whole #s.

  10. Examples Find 17 ¼ - 3 5/8 17 ¼ - 3 5/8

  11. Examples Find 17 ¼ - 3 5/8 17 ¼ 17 2/8The LCM of 4 & 8 is 8 - 3 5/8- 3 5/8

  12. Examples Find 17 ¼ - 3 5/8 17 ¼ 17 2/8 The LCM of 4 & 8 is 8 - 3 5/8- 3 5/8 17 2/8 16 10/8 Since 5/8 is greater - 3 5/8- 3 5/8 than 2/8 you must rename 17 2/8 as 16 10/8

  13. Examples Find 17 ¼ - 3 5/8 17 ¼ 17 2/8 The LCM of 4 & 8 is 8 - 3 5/8- 3 5/8 17 2/8 16 10/8 Since 5/8 is greater - 3 5/8- 3 5/8 than 2/8 you must rename 17 2/8 as 16 10/8 16 10/8 Subtract the fractions - 3 5/8 then subtract the whole 13 5/8 #s.

  14. Examples A male California sea lion grows to be between 6 ½ and 8 feet long. Find the difference between the greatest and least lengths. 8 - 6 ½

  15. Examples A male California sea lion grows to be between 6 ½ and 8 feet long. Find the difference between the greatest and least lengths. 8 7 2/2 Rename 8 as 7 2/2 - 6 ½- 6 ½

  16. Examples A male California sea lion grows to be between 6 ½ and 8 feet long. Find the difference between the greatest and least lengths. 8 7 2/2 Rename 8 as 7 2/2 - 6 ½- 6 ½ 1 ½ Subtract the fractions then subtract the whole #s.

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