Advanced Arithmetic

before operations indicated by + and

Thus, in 8+6

× 2, first multiply 6 by 2, and then add their product to 8. 8+6x2=8+12=20.

23. Which is larger, 10+ 10+10 or 10 10+10?

24. Show that 42 ÷ 6 +7 is equal to 42 - 7 x 4. 25. What is the value of 4x5+6x7-8÷4? 26. What is the sum of 66 +6 +5 and 66 - 5 x 10? 27. What is the product of 8 +56 +8 and 56-12 × 4? 28. How many times is 32÷8+5 contained in 32+ 8 x 5?

2. What factors are common to both dividend and divisor?

3. Does striking out or canceling equal factors from both dividend and divisor affect the quotient?

Divide:

4. 12 × 10 × 9 by 4 × 5

5. 24 x 15 x 6 by 8 × 5 × 3
6. 14 x 20 x 6 by 7 x 10 x 2
7. 18 × 60 × 15 by 9 × 5 × 20
8. 15 × 44 × 18 by 22 × 5 × 9

9. 36 x 32 x 16 by 24 x 3 x 8

10. 64 x 35 x 42 x 40 by 8 × 56 × 12 × 10

11. 72 × 81 × 45 × 28 by 90 × 144 × 63

Beginning with any number in the margin and going in either direction, rapidly add the numbers until 100 or any given number is reached.

Beginning with 100 or any given number, rapidly subtract the successive numbers.

9 4 12 7 20 15 8 6

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11 8

FRACTIONS

A unit is a single thing; as 1 apple.

A fraction is one or more of the equal parts of a unit; as of an apple.

of an apple means that an apple has been divided into 4 equal parts and 3 of these parts taken.

In a fraction:

(1) The figure below the line is the denominator; it denominates or names the number of equal parts into which the unit is divided; it is the namer.

(2) The figure above the line is the numerator; it numerates or tells the number of parts taken; it is the numberer.

The numerator and denominator are the terms of the traction.

1. In the fraction:

(1) What is the 6 called? (2) What is the 5 called?

(3) What does the fraction

What does it show?
What does it show?
show?

2. Read aloud and tell what the terms of each fraction

Oral

CHANGING THE FORM OF FRACTIONS

1. Which do you prefer, of a dollar or of a dollar?

g of a pound of candy or

2. Are and alike

of a pound of candy?

in form? Are they alike in

3. Are and alike in value? In form? 4. How many equal parts in of a dollar? 5. How many equal parts in & of a dollar?

6. What is the size of the equal parts in of a dollar? 7. What is the size of the equal parts in § of a dollar? 8. Are 8ths of a dollar larger or smaller than 4ths of a dollar?

In & of a dollar there are twice as many equal parts as in of a dollar, but the equal parts are only one half as large.

In of a dollar there are one half as many equal parts as in § of a dollar, but the equal parts are twice as large. The form of a fraction may be changed without changing its value:

(1) By multiplying both terms of the fraction by the same number.

This is changing to higher terms.

(2) By dividing both terms of the fraction by the same number.

CHANGING TO HIGHER TERMS

1. Change to twenty-fourths.

To get 24 as the denominator, we multiply the denominator by 3. In order not to change the value of the fraction, we also multiply the numerator by 3.

To change a fraction to higher terms, multiply both terms of the fraction by that number which will give the required denominator.