## Math Expressions Common Core Grade 4 Unit 8 Lesson 1 Answer Key Points, Rays, and Angles

**Math Expressions Grade 4 Unit 8 Lesson 1 Homework**

**Draw each geometric figure.**

Question 1.

a point

Answer:

Explanation:

A point is a dot on plan.

Question 2.

a ray

Answer:

Explanation:

A ray has one starting point and no end point.

Question 3.

an angle

Answer:

Explanation:

An angle is the is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Question 4.

Name the angle shown.

Answer:

Angle GNL

Explanation:

an angle is the is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

**Look at the angles below.**

Question 5.

Which angles are right angles?

Answer:

P and Z

Explanation:

A right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

Question 6.

Which angles are acute angles?

Answer:

M and V

Explanation:

An acute angle is an angle that measures between 90° and 0**°**, meaning it is smaller than a right angle (an “L” shape) but has at least some space between the two lines that form it.

Question 7.

Which angles are obtuse angles?

Answer:

A and T

Explanation:

Angles measuring greater than 90° and less than 180° are called obtuse angles.

**Math Expressions Grade 4 Unit 8 Lesson 1 Remembering**

**Add or subtract.**

Question 1.

Answer: 9

Explanation:

i) Write the mixed fraction as fractions

ii) Add the fractions

iii) Convert the fraction in to mixed fraction

Question 2.

Answer: 8 \(\frac{2}{8}\)

Explanation:

i) Write the mixed fraction as fractions

ii) Subtract the fractions

iii) Convert the fraction in to mixed fraction

Question 3.

Answer:

13 \(\frac{1}{7}\)

Explanation:

i) Write the mixed fraction as fractions

ii) Add the fractions

iii) Convert the fraction in to mixed fraction

Question 4.

Answer:

3 \(\frac{6}{9}\)

Explanation:

i) Write the mixed fraction as fractions

ii) Subtract the fractions

iii) Convert the fraction in to mixed fraction

**Write < or > to make each statement true.**

Question 5.

\(\frac{3}{4}\) \(\frac{1}{4}\)

Answer:

\(\frac{3}{4}\) **>** \(\frac{1}{4}\)

Explanation:

Recall that the symbol < means “less than”, and the symbol > means “greater than”.

These symbols are inequality symbols.

In the above sum \(\frac{3}{4}\) contains more parts of the whole than \(\frac{1}{4}\)

So,\(\frac{3}{4}\) **>** \(\frac{1}{4}\)

Question 6.

\(\frac{5}{6}\) \(\frac{5}{4}\)

Answer:

\(\frac{5}{6}\) **<** \(\frac{5}{4}\)

Explanation:

To compare the unequal fraction, make the denominators same by multiplying the numerator and the denominator with same number, then compare

\(\frac{5}{6}\) x \(\frac{4}{4}\) = \(\frac{20}{24}\)

\(\frac{5}{4}\) x \(\frac{6}{6}\) = \(\frac{30}{24}\)

\(\frac{20}{24}\) < \(\frac{30}{24}\)

\(\frac{5}{6}\) **<** \(\frac{5}{4}\)

Question 7.

\(\frac{7}{10}\) \(\frac{7}{12}\)

Answer:

\(\frac{7}{10}\) **>** \(\frac{7}{12}\)

Explanation:

To compare the unequal fraction, make the denominators same by multiplying the numerator and the denominator with same number, then compare

\(\frac{7}{10}\) x \(\frac{12}{12}\) = \(\frac{84}{120}\)

\(\frac{7}{12}\) x \(\frac{10}{10}\) = \(\frac{70}{120}\)

\(\frac{84}{120}\) > \(\frac{70}{120}\)

\(\frac{7}{10}\) > \(\frac{7}{12}\)

Question 8.

\(\frac{6}{8}\) \(\frac{4}{8}\)

Answer:

\(\frac{6}{8}\) **>** \(\frac{4}{8}\)

Explanation:

Recall that the symbol < means “less than”, and the symbol > means “greater than”.

These symbols are inequality symbols.

In the above sum \(\frac{6}{8}\) contains more parts of the whole than \(\frac{4}{8}\)

So,\(\frac{6}{8}\) **>** \(\frac{4}{8}\)

Question 9.

\(\frac{4}{8}\) \(\frac{4}{12}\)

Answer:

\(\frac{4}{8}\) **>** \(\frac{4}{12}\)

Explanation:

To compare the unequal fraction, make the denominators same by multiplying the numerator and the denominator with same number, then compare

\(\frac{4}{8}\) x \(\frac{12}{12}\) = \(\frac{48}{96}\)

\(\frac{4}{12}\) x \(\frac{8}{8}\) = \(\frac{32}{96}\)

\(\frac{48}{96}\) > \(\frac{32}{96}\)

\(\frac{4}{8}\) **>** \(\frac{4}{12}\)

Question 10.

\(\frac{17}{25}\) \(\frac{21}{25}\)

Answer:

\(\frac{17}{25}\) **< **\(\frac{21}{25}\)

Explanation:

Recall that the symbol < means “less than”, and the symbol > means “greater than”.

These symbols are inequality symbols.

In the above sum \(\frac{17}{25}\) contains less parts of the whole than \(\frac{21}{25}\)

So,\(\frac{17}{25}\) < \(\frac{21}{25}\)

Question 11.

Mark and label the point for each fraction or mixed number with its letter.

a. 2\(\frac{1}{2}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 2 whole number 4th part is marked as \(\frac{1}{2}\)

b. 3\(\frac{5}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

After 3 whole number 5th part is marked as \(\frac{5}{8}\)

c. \(\frac{1}{4}\)

Answer:

Explanation:

First draw a number line, mark the given number on the number line. Between 0 to 1, number 2nd part is marked as \(\frac{1}{4}\)

d. 1\(\frac{4}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

After 1 whole number 4th part at center is marked as \(\frac{1}{2}\)

e. 3\(\frac{1}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

After 3 whole number 1st part is marked as \(\frac{1}{8}\)

f. 2\(\frac{3}{4}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

After 2 whole number 6th part is marked as \(\frac{3}{4}\)

g. 3\(\frac{1}{2}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 3 whole number 4th part at center is marked as \(\frac{1}{2}\)

h. 1\(\frac{7}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

After 1 whole number 7th part is marked as \(\frac{7}{8}\)

i. \(\frac{6}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

First 0 to 1 is sub divided in to 8 parts, 6th part is marked as \(\frac{6}{8}\)

j. 4\(\frac{3}{8}\)

Answer:

Explanation:

First draw a number line, and then mark the given numbers on the number line.

4\(\frac{3}{8}\) come after 4 whole numbers, mark 3rd part in 8 parts.

Question 12.

**Stretch Your Thinking** Two spiders sit on the upper left corner of a window frame. One spider starts walking right along the top of the window frame. The other spider starts walking down along the left side of the window frame. Name each of the following using geometry terms.

a.) the place where the spiders began _____________

Answer:

Point or Origin point

Explanation:

A point is a dot on plan.

b.) the walking path of each spider ___________

Answer:

Ray

Explanation:

A ray has one starting point and no end point

c.) the type of angle formed by their paths ____________

Answer:

Right angle

Explanation:

A right angle is an angle with a value equal to 90°.

When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection.