Visual Models for Fraction Operations
- 1. Visual Models forFraction Operations
- 2. Addition+
- 3. Addition of Fractions: For any fractions a/b and c/d, a + c = ad + bc = ad + bcb d bdbdbd
- 4. Approximating Method when Adding Fractions_3_4_1_2_1_ 3When the two shaded amounts are combined, the total is approximately . _3_4
- 5. Finding the sum of two fractions is easy when they have the same denominator. 4_ 6 3_ 6 4_ 6 3_ 6 7_ 6 1_ 6=1+OR
- 6. Addition of fractions can also be illustrated using a number line:
- 7. Adding Unlike Denominators¼ + ⅓ = ?
- 8. First, find the smallest common denominator of ¼ and ⅓.1 × 3 = _3_ 3 121 × 4 = _4_3 4 121 = _3_4 121 = _4_3 12So…
- 9. 1 + 14 3=_3_ + _4_ 12 12=_7_ 121 + 1 = _7_4 3 12
- 10. Subtraction_
- 11. Subtraction of Fractions: For any fractions a/b and c/d, a _ c = ad _ bc =ad – bcb d bdbdbd
- 12. Using a Number Line:
- 13. Using Fraction Bars:_1_ _1_ _2_ _1_ 2 6 6 3_=OR 1_ 2_1_ 6_1_ 3
- 14. Subtracting Unlike Denominators:This is what’s left over._5_ 6_1_ 4_5_ _1_ 6 4 _= ?…
- 15. …The smallest common denominator of ⅚ and ¼ is 12.• 5 × 2 = 101 × 3 = 3 6 2 12 4 3 12 • 10 - 3 = 7 12 12 121012 312 712
- 16. Multiplication×
- 17. Whole Number Times a Fraction: For any whole number k and fraction a/b, k × a = ka b b
- 18. Multiplication of a fraction and a whole number can be illustrated in a couple of different ways.
- 19. Whole Number Times a Fraction1 Whole Bar3 × 1 = 1 + 1 + 1 = 3 or 1 1_ 2 2 2 2 2 2
- 20. Fraction Times a Whole NumberABC 1 × 4 = 1 + 1 + 1 + 1 = 4_ 3 3 3 3 3 3
- 21. Fraction Times a Whole Number 1⅓ 1 1 3 3× 4 =1
- 22. Multiplication of Fractions: For any fractions a/b and c/d,a× c = ac b d bd
- 23. Fraction Times a Fraction1_ 5×1_ 3 1_15 1 × 1 = 1_ OR 1 of 1 = 1_ 3 5 15 3 5 15 1_15
- 24. Fraction Times a Fraction4_5×2_3 8_15 2 × 4 = 8_ OR 2 of 4 = 8_ 3 5 15 3 5 15 8_15
- 25. Division÷
- 26. Division of Fractions: For any fractions a/b and c/d, with c/d ≠ 0,a ÷ c = a × d = adb d b c bc
- 27. 5 ÷ 1_ 6 12_1_12_5_6goes into 10 times. = 10…
- 28. 5 ÷ 1__1_ 6 3 2= 2RemainderDivisor
- 29. Inverting the Divisor and MultiplyingTRIPLE BOTH AMOUNTS)) 1 1 1_ 1_ 3_ 3_ 2 3 2 3 2 2((===÷× 3÷× 3÷ 1Simplified Version of Equation Above 1 1 1 3 3 1_ 2 3 2 1 2 2 == 1×÷=