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Lesson 10

MIXED CALCULATION OF THREE FRACTIONS

A. Objectives

Students will be able to:

1. Understand and perform mixed calculations involving addition, subtraction, and multiplication of three fractions.

B. Instructional Content and Activities

Mixed calculation: Addition and multiplication

Students will study the calculation method for (	2	+	1	) × 9.
	5		3

( 2 + 1 ) × 9 5 3	=	( 6 + 5 ) × 9 15 15		Find the common denominator for the fractions (inside parentheses).
	=	6 + 5 × 9 15		Add the two fractions.
	=	3 11 × 9 15 5		Reduce, then multiply.
	=	33 = 6 3 5 5		If improper, change to a mixed number.

Be sure students understand that the operation inside the parentheses is calculated first. The fractions could also be multiplied separately, as below, but this is not recommended.

3   ( 2 × 9) + ( 1 × 9 ) 5 3   1	=	18 + 3 5
	=	3 3 + 3 5
	=	6 3 5

Point out that the result is the same as the previous calculation.

Mixed calculation: Subtraction and multiplication

Students next study the calculation method for (	1	-	2	) ×	3	.
	3		7		5

( 1 - 2 ) × 3 3 7 5	=	( 7 - 6 ) × 3 21 21 5		Find the common denominator for the fractions inside the parentheses.
	=	7 - 6 × 3 21 5		Find the difference of the fractions inside the parentheses.
	=	1 1 × 3 21 5 7		Reduce.
	=	1 = 1 7 × 5 35		Express as a multiplication; calculate.

C. Teaching and Evaluation Tips

Teaching tip

• It is important for students to know the order of operations when calculating. They should understand that the calculation inside the parentheses is performed first. The distributive laws are not used here.

Evaluation tip

• Using the distributive laws is not evaluated in the calculation order that is the basic calculation in the mixed calculation of three fractions.