Math Problem Statement

A set of various mathematical questions, including topics such as mixed numbers, decimal multiplication, fractions, percentages, and solving equations.

Solution

I'll go through the questions in the uploaded image and help you solve them step by step.

1. Write as a mixed number:

  • a)115a) \, \frac{11}{5}
  • b)238b) \, \frac{23}{8}
  • c)199c) \, \frac{19}{9}

2. Evaluate, giving your answer in lowest terms:

  • a)128a) \, 12 - 8
  • b)4×(73)b) \, 4 \times (7 - 3)
  • c)36(14)9×2+3c) \, \frac{36 - (1-4)}{9 \times 2 + 3}

3. Find:

  • a)335+112a) \, 3 \frac{3}{5} + 1 \frac{1}{2}
  • b)0.56+1.952b) \, 0.56 + 1.952
  • c)61.3÷4c) \, 61.3 \div 4

4. 78\frac{7}{8} of Peter’s garden beds are used to grow fruit and vegetables. Of these, 14\frac{1}{4} of the growing space is taken up by eggplants. What fraction of Peter’s garden beds is taken up by eggplants?

5. Place the decimals 0.2,0.6,0.4,1.1,1.30.2, \, 0.6, \, -0.4, \, 1.1, \, -1.3 on a number line.

6. Write as a fraction in lowest terms:

  • a)0.22a) \, 0.22
  • b)0.06b) \, 0.06
  • c)0.0092c) \, 0.0092

7. Multiply 0.03580.0358 by:

  • a)10a) \, 10
  • b)100b) \, 100
  • c)1000c) \, 1000

8. Find:

  • a)0.12×0.07a) \, 0.12 \times 0.07
  • b)3+0.6b) \, 3 + 0.6
  • c)1.967÷0.07c) \, 1.967 \div 0.07

9. Mrs. Austen is having trouble with her printer. The first quarter of her book is printed in red, the next sixth in blue, the next twelfth in green, and all the rest in black.

  • a)a) What fraction of the book has black printing?
  • b)b) The book has 252 pages. What page numbers are in blue?
  • c)c) Some of these pages were also erased. Find, in simplest terms, the fraction of pages that were erased.

10. Without using your calculator, write 56\frac{5}{6} as a recurring decimal.

11. Between which two consecutive integers does 75\sqrt{75} lie?

12. Use your calculator to find, correct to 3 decimal places if necessary:

  • a)1831a) \, \sqrt{1831}
  • b)7800b) \, \sqrt{7800}

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Math Problem Analysis

Mathematical Concepts

Mixed Numbers
Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
Decimals
Fractions
Number Line Placement
Proportion and Ratio
Square Roots
Recurring Decimals
Basic Algebra

Formulas

a + b (Addition)
a - b (Subtraction)
a × b (Multiplication)
a ÷ b (Division)
Fraction Conversion to Mixed Number
√n (Square Root)

Theorems

Basic Properties of Fractions
Decimal to Fraction Conversion

Suitable Grade Level

Grades 6-8