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## 180 Days of Math for Fifth Grade Answers Key Day 147

**Directions: Solve each problem.**

Question 1.

76 + 62 = ___________

Answer:

The addition is the term used to describe adding two or more numbers together. The addition is denoted using the plus sign ‘+‘ such as the addition of 3 and 3 can be written as 4 + 4. Also, the plus sign (+) can be used as many times as required, such as

4 + 4 + 4 + 4.

Therefore, the answer is 138.

Question 2.

Answer:

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ a number of times or vice versa.

The formula for multiplication:

The multiplication formula is given by:

Multiplier × Multiplicand = Product

– The multiplicand is the total number of objects in each group

– A multiplier is the number of equal groups

– Product is the result of multiplication of multiplier and multiplicand

Therefore, the answer is 516.

Question 3.

Answer:

The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √9 = 3. The radical symbol is also called a root symbol or surds. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.

– Here we will show you how to calculate the square root of 825 using the long division method with one decimal place accuracy.

The answer is on top. The square root of 825 with one digit decimal accuracy is 28.722. Did you notice that the last two steps repeat the previous two steps? You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.

therefore, the square root of 825 is 28.722

The above-given question is 5 square root of 28.722 is:

We got a square root of 825 is 28.722

Now multiply 5 by 28.722

Thus, 5*28.722 is 143.61

Question 4.

Is 5,849 greater than or less than 6,849?

Answer:

5,849 is less than 6,849

Greater than and less than symbols are used to compare any two numbers. When a number is bigger than or smaller than another number, greater than less than symbols are used. If the first number is greater than the second number, greater than symbol (>) is used. If the first number is less than the second number, less than symbol (<) is used.

Now check the first left-side in both the numbers and check.

5 is less than 6. According to the above information

5,849 < 6,849.

Question 5.

Calculate half of $9.70.

Answer: $4.85

Explanation:

Half of $9.70 = Half of $9 + half of $.50

= $4.5 + $3.5

= $4.85

or else,

we can divide by 2.

$9.70/2 = $4.85

Question 6.

72 ÷ 8 + 25 × 3 = __________

Answer:

The value of 72 ÷ 8 is 9.

The value of 25 × 3 is 75

Now add the values we got. Let the answer be X.

X = 9 + 75

X = 84.

Therefore, the value of the above-given equation is 84.

Question 7.

42 × 1 = 42 +

Answer:

Let us assume the empty box is X.

42 × 1 = 42 + X

42 = 42 + X

Now get 42 to the left-hand side then the equation will be:

42 – 42 = X

0 = X

Therefore, the value of X is 0.

Now verify the answer by putting the X value in the above-given equation.

42 × 1 = 42 + X

42 = 42 + 0

42 = 42

Left-hand side = right-hand side.

Hence, the answer is verified.

Question 8.

What is the line length in centimetres?

Answer: 3.5 cms

– Like the inches ruler, you’ll see tons of lines on a metric ruler, with some longer and some shorter. Each line represents 1 millimeter, which is equal to 1/10 or 0.1 cm (so 10 mm make up 1 cm).

– There will always be 10 lines from one centimeter to the next centimeter. In total, there are three different lengths of lines on a metric ruler.

– The longest line represents the biggest unit on the ruler: 1 cm. Each centimeter is labeled on the ruler (1-30).

– The middle-length line on a metric ruler is the 1/2 (0.5) centimeter line, which comes midway between every centimeter (in other words, it’s the fifth line after every whole centimeter):

– Now observe the above-given picture if you count 5 lines from 3 cms then you would get 3.5 cm.

Question 9.

What is the sum of the inside angles of a triangle?

Answer:

The sum of interior angles of a triangle is always equal to 180°. This is because, if we join the three interior angles of the triangle, we will form a straight line. This property can be used to find the different measures of the three interior angles of the triangle.

Question 10.

What is the outlier in this data set?

278, 324, 353, 125, 314

Answer:

There is no outlier.

The step-by-step calculation for outliers:

First, we have to arrange it in ascending order.

125, 278, 314, 324, 353

N = 5 (odd)

An outlier in distribution is a number that is more than 1.5 times the length of the box away from either the lower or upper quartiles. Speciﬁcally, if a number is less than Q1 – 1.5×IQR or greater than Q3 + 1.5×IQR, then it is an outlier.

– The first quartile, also called the lower quartile, is equal to the data at the 25th percentile of the data. The third quartile also called the upper quartile, is equal to the data at the 75th percentile of the data.

Median(Q2) = 314

If the N value is odd then no need to take the median.

Q1 = 125+278/2

Q1 = 403/2

Q1 = 201.5

Q3 = 324+353/2

Q3 = 677/2

Q3 = 338.5

Interquartile range: the interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the third quartile (Q3) and first quartile (Q1), that is, IQR = Q3 – Q1.

IQR = 338.5-201.5

IQR = 137

Now check the outliers:

Q1 – 1.5 * IQR

201.5 – 1.5 * 137 = -4

Q3 + 1.5 * 410

338.5 + 1.5 * 410=953.5

Now once observe the data set and see if there are any values less than -4 and greater than 953.5

125, 278, 314, 324, 353

There are no values so there are no outliers.

Question 11.

Imagine that you write each letter of the word CALIFORNIA on individual cards. You shuffle them, turn them facedown on a table, and turn over the top card. What is the probability of turning over one of the first three letters of the alphabet?

Answer:

This formula is the number of favourable outcomes to the total number of all the possible outcomes that we have already decided in the Sample Space.

The probability of an Event = (Number of favourable outcomes) / (Total number of possible outcomes)

P(A) = n(E) / n(S)

P(A) < 1

Here, P(A) means finding the probability of an event A, n(E) means the number of favourable outcomes of an event and n(S) means the set of all possible outcomes of an event.

The total number of possible outcomes=10

The number of favourable outcomes=3

P(first three letters)=3/10.

Therefore, the probability is 3/10

Question 12.

Find and color 5 parallelograms within the image below.

Answer:

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called Parallelogram. The properties of the parallelogram are:

– The opposite sides are parallel and congruent

– The opposite angles are congruent

– The consecutive angles are supplementary

– If any one of the angles is a right angle, then all the other angles will be at a right angle

– The two diagonals bisect each other

– Each diagonal bisects the parallelogram into two congruent triangles

– The Sum of squares of all the sides of a parallelogram is equal to the sum of squares of its diagonals. It is also called parallelogram law.