2. 35 Adding Fractions Add 1 1 2 Estimate the sum x = 5 5 8 8 40 32 40 67 = 12740 Find the least common denominator ~...(find the LCM of 8 and 5).. ~ 8: 8, 16, 24, 32, 40 ~ 5: 5, 10, 15, 20, 25, 30, 35, 40 ~ The LCM is 40. Change both denominators to 40...then change both numerators Add the new numerators, then keep the denominator the same. mixed number Convert to a mixed number. Is the sum close to the estimate? 40

3. Adding Fractions

4. 18 Adding Mixed Numbers Add 2 4 6 Estimate the sum x = 2 2 5 5 20 5 23 = 1 320 Find the least common denominator ~...(find the LCM of 10 and 4).. ~ 10: 10, 20, 30, 40 ~ 4: 4, 8, 12, 16, 20... ~ The LCM is 20. Change both denominators to 20...then change both numerators Add the new numerators, then keep the denominator the same. mixed number Convert to a mixed number. Is the sum close to the estimate? 20 9 10 1 1414 4 Add the whole numbers to the sum. + 5 6 320

5. 39 Subtracting Fractions Subtract 1 1 0 Estimate the difference x = 3 3 7 7 42 35 42 4 221 Find the least common denominator ~...(find the LCM of 14 and 6) ~ 14: 14, 28, 42, 56, 70, 84... ~ 6: 6, 12, 18, 24, 30, 36, 42... ~ The LCM is 42. Change both denominators to 42...then change both numerators Subtract the new numerators, then keep the denominator the same. Simplify by finding the GCF ~ 4: 1, 2, 4 ~ 42: 1, 2,... Is the sum close to the estimate? 42 13 14 – 5656 – ÷ = 2 2 –

6. Subtracting Fractions

7. Rewrite each mixed number by borrowing. 4 9 4 Take one from 4 (now you have 3...)...then add it back to the fraction \ 3 9999 + = 13 9 3 Remember: 1 = 9999 Subtracting Mixed Numbers 7 11 2 18 11 1 = 2323 1 5353 = 5959 8 14 9 7 = 3838 10 11 8 9 =

8. 16 Subtracting Mixed Numbers 8 7 1 Estimate the difference x = 8 8 3 3 24 21 24 19 19 24 24 Find the least common denominator ~...(find the LCM of 3 and 8).. ~ 3: 3, 6, 9, 12, 15, 18, 21, 24 ~ 8: 8, 16, 24 ~ The LCM is 24. Change both denominators to 24...then change both numerators Subtract the new numerators, then keep the denominator the same. 2323 7 7878 6 – To avoid negative fraction, let’s borrow from the whole number Take one from 7 (now you have 6...)...then add it back to the fraction \ 6 24 += 40 24 – Is the estimate close to the difference?

9. Adding Mixed Numbers Subtracting Mixed Numbers

10. 4 9 4 9 Estimate the product.  4 9 = 36 Convert each to a simple fraction 40 9 1 = \ \ 1 1 40 1 = 40 Cross-simplify. Multiply numerators, then denominators Simplify the product. Multiplying Fraction and Mixed Numbers 40 9 1

11. Multiplying Fraction and Mixed Numbers

12. Dividing Fractions and Mixed Numbers 1. 4747 4747 7474 2.1010 1 11 8 1 10 8 11 3. 3838 1 Original number FractionReciprocal 4. 1212 = 2 5. 6 1616 = 6. 1 = 1 7. 2525 1 5757 =

13. 3 8 5 ÷ 9 Estimate the quotient.  5 ÷ 9  1212 Convert each to a simple fraction 5 1 ÷ 75 8 = \ \ 1 17 17 8 17 Cross-simplify. Multiply numerators, then denominators Dividing Fractions and Mixed Numbers 5151 8 75 Keep the first fraction the same Change the division to multiplication Flip the 2 nd fraction

14. Dividing Fractions and Mixed Numbers