Properties of Addition and Subtraction of Integers

Sana and Fatima participated in an apple race. The race was conducted in $6$ parts. In the first part, Sana won by $10$ seconds. In the second part she lost by $1$ minute, then won by $20$ seconds in the third part and lost by $25$ seconds in the fourth part, she lost by $37$ seconds in the fifth part and won by $12$ seconds in the last part. Who won the race finally?

Social Studies Application: Remembering that $1\mathrm{AD}$ came immediately after $1\mathrm{BC},$ while solving these problems take $1\mathrm{BC}$ as $-1$and $1\mathrm{AD}$ as $+1$

Bhaskaracharya was born in the year $1114 \mathrm{AD}$ and died in the year $1185 \mathrm{AD}$. What was his age when he died in years?

Social Studies Application: Remembering that $1\mathrm{AD}$ came immediately after $1\mathrm{BC},$ while solving these problems take $1\mathrm{BC}$ as $-1$and $1\mathrm{AD}$ as $+1$

The Greeco-Roman era, when Greece and Rome ruled Egypt started in the year $330\mathrm{BC}$ and ended in the year $395 \mathrm{AD}$. How long did this era last in years?

The highest point measured above sea level is the summit of Mt. Everest which is $8,848$m above sea level and the lowest point is challenger Deep at the bottom of Mariana Trench which is$10911$m below sea level. If the vertical distance between these two points is $k \mathrm{m}$, find the value of $k$.

Taking today as zero on the number line, if the day before yesterday is $17$ January, what is the date $3$ days after tomorrow?

In a test , $+3$ marks are given for every correct answer and $-1$ mark are given for every incorrect answer. Sona attempted all the questions and scored $+20$ marks though she got $10$correct answers.

How many questions were given in the test?

In a test , $+3$ marks are given for every correct answer and $-1$ mark are given for every incorrect answer. Sona attempted all the questions and scored $+20$ marks though she got $10$correct answers.

How many incorrect answers has she attempted?

A green grocer had a profit of$₹47$ on Monday, a loss of$₹12$ on Tuesday and loss of$₹8$ on Wednesday. If his net profit or loss in $3$ days is $₹k$, find the value of $k$.

Height of a place $A$ is $1800 \mathrm{m}$ above sea level. Another place $B$ is $700 \mathrm{m}$ below sea level. If the difference between the levels of these two places is $k \mathrm{m}$, find the value of $k$.

The given table shows the freezing points in $°F$ of different gases at sea level. Convert each of these into $°C$ to the nearest integral value using the relation and complete the table,

$C=\frac{5}{9}(F-32)$

$\begin{array}{|lcc|}\hline \text{ Gas }& \begin{array}{c}\text{ Freezing Point at }\\ \text{ Sea Level }\left({}^{\circ }\mathbf{F}\right)\end{array}& \begin{array}{c}\text{ Freezing Point at }\\ \text{ Sea Level }\left({}^{\circ }\mathbf{C}\right)\end{array}\\ \text{ Hydrogen }& -435& \\ \text{ Krypton }& -251& \\ \text{ Oxygen }& -369& \\ \text{ Helium }& -458& \\ \text{ Argon }& -309& \\ \hline\end{array}$

What's the Error? Reeta evaluated $-4+d$ for $d=-6$ and gave an answer of $2$. What might Reeta have done wrong?

What's the Error? Ramu evaluated the expression $-7-(-3)$ and came up with the answer $-10$ What did Ramu do wrong?

Write two integers such that one is smaller than $-11$, and other is greater than $-11$ but their difference is $-11$

Write two negative integers whose difference is $7$

Write two integers which are smaller than $-6$ but their difference is greater than $-6$.

Write two integers which are greater than$-4$ but their difference is smaller than $-4$

Write two integers which are greater than $-10$ but their sum is smaller than $-10$.

Write two integers which are smaller than $-5$ but their difference is $-5$.

Write a positive integer and a negative integer whose difference is a positive integer.

Write a positive integer and a negative integer whose difference is a negative integer.